Mathematician’s Day: Professor highlights data compression algorithms’ potential for mathematics
Mathematics can explain both the sources of problems and solutions to them. Every challenge, whether in the area of finance, politics, safety or health, can be represented by mathematical models. Today, October 26, is Mathematician’s Day in Brazil. To mark this day, FGV News interviewed Professor Vicent Guigues of Fundação Getulio Vargas’ School of Applied Mathematics (FGV EMAp).
Applied mathematics is a branch of mathematics that intersects with various fields of knowledge, providing banks, retailers and internet companies with algorithms to innovate.
In this interview with FGV News, Professor Guigues stresses applied mathematics’ ability to deal with a huge amount of data and solve problems that couldn’t be solved with just pen and paper. He also highlights Google’s PageRank algorithm, programming languages and GPS’ impact in the digital age.
How has digital acceleration affected applied mathematics?
To answer this question, we first have to define digital acceleration. I understand this concept to mean the development of the internet and computing, the growth of computers, ever faster smartphones and hard drives able to store large amounts of data.
In particular, the arrival of computers allowed us to solve mathematical problems that we simply couldn’t solve with just pen and paper.
The development of increasingly fast computers enabled us to tackle large-scale mathematical problems in areas such as differential equations, optimization and statistics.
What new tools has digital acceleration brought to this area?
We can now use computers to solve differential equations that model the evolution of time. In addition, it is possible to use technology to solve large optimization problems that model real-life applications, such as passive asset management in the finance sector and routing problems in logistics.
For example, Amazon has a large operational research group to model its routing problems and determine delivery strategies.
How has digital acceleration benefited applied mathematics?
I would say that all areas of applied mathematics have benefited from digital acceleration, which has allowed us to solve large mathematical problems, in particular by using cloud computing and GPU programming.
Nowadays we can think of intelligent systems that handle data in real time. One example of this is phone apps like Uber. The new challenge for professionals in this area is to develop algorithms to speed up rides in real time. This involves car choice strategies and vehicle routing algorithms. In particular, they can use area-specific strategies to automatically learn of roadworks and decide the best times to use certain roads.
What was applied mathematics like before digital acceleration?
Before digital acceleration, we were limited in terms of the size of the problems we could solve. The use of statistical differential equations was also limited before the arrival of computers. We couldn’t solve large optimization problems and we could only solve problems manually, like variables.
What is digital acceleration’s main challenge for the profession and what is its main benefit?
The main challenge, for both users and applied mathematicians, is to keep up with new technologies, identify technologies that may be useful and learn to use them.
The main benefit is being able to solve more realistic problems of larger size, in particular using big data and real-time data.
How has applied mathematics contributed to digital acceleration?
Mathematics has played a fundamental role since the beginning of computing, for example in terms of logic, the development of compilation grammars, discrete mathematics, automata theory and cryptography.
I could mention many specific cases in which applied mathematics has contributed to digital acceleration, such as the development of Google’s PageRank algorithm. This algorithm calculates a weighting for each web page, indicating its importance. It is an interpretation of how likely a user would be to enter this page. Accordingly, the algorithm calculates an eigenvector associated with the transition matrix.
A second good example of applied mathematics’ impact in the digital age is GPS. Without a doubt, GPS has changed our lives and it is present in many applications. It solves a least squares problem to determine our location, using information provided by four satellites.
How has the education of new mathematicians been changing?
First, we are placing greater emphasis on statistical probability. It’s a fact that our society is generating more and more data and we are able to collect it in real time. To explain this data, we need statistical and probabilistic models.
Second, it is now more important to have good programming skills. So, these days, applied mathematicians must know multiple programming languages.
Third, I believe it is fundamental to learn how to learn. This is especially important, given that we now look for information online and we have an almost infinite amount of information on the internet.
Fourth, distance learning has been growing. This means that applied mathematicians can take online courses and learn on their own.
Learn about FGV EMAp’s undergraduate courses.
This article is part of a special series called Connections for the Future, which began on July 22, which in Brazil is Social Scientist’s Day.